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3 years ago

Help please

Mathematics

2 answers:

weqwewe [10]3 years ago

5 0

Answer:

17.7 ft

Step-by-step explanation:

Let x be the shorter leg

Longer: x + 7

Hypotenuse: 2x - 5

(2x - 5)² = (x + 7)² + x²

4x² - 20x + 25 = x² + 14x + 49 + x²

2x² - 34x - 24 = 0

x² - 17x - 12 = 0

x = [17 +- sqrt(17² - 4(1)(-12)]/2

x = [17 + sqrt(337)]/2

x = 17.67877988

Natali5045456 [20]3 years ago

4 0

Answer:

17 ± sqrt(337)

-----------------------

Step-by-step explanation:

Let a = shorter leg

b= longer leg = a+7

c = hypotenuse = 2a-5

We can use the Pythagorean theorem

a^2+b^2 = c^2

a^2 + (a+7)^2 = (2a-5)^2

(a+7)^2 = a^2 +7a +7a+49 = a^2 +14a +49

(2a-5)^2 = 2a*2a -10a -10a +25 = 4a^2 -20a +25

Substituting these into the equation

a^2 + (a^2 +14a +49) = (4a^2 -20a +25)

Combine like terms

2a^2 +14a +49 = 4a^2 -20a +25

Subtracting 2a^2 from each side

2a^2 -2a^2 +14a +49 = 4a^2-2a^2 -20a +25

+14a +49 = 2a^2 -20a +25

Subtract 14a from each side

-14a+14a +49 = 2a^2 -20a -14a+25

+49 = 2a^2 -34a +25

Subtract 49 from each side

49-49 = 2a^2 -34a +25-49

0 = 2a^2 -34a -24

Divide each side by 2

0/2 = 2/2a^2 -34/2a -24/2

0 = a^2 -17a -12

Using the quadratic formula

a=1 b= -17 c = -12

17 ±sqrt( (-17)^2 - 4(1)(-12))

----------------------------------

2(1)

17 ± sqrt(337)

-----------------------

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3 years ago

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dybincka [34]

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3 years ago

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jolli1 [7]

Answer:

GIVEN BY POINTS :-

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Using Distance formula :

$= > \sf d = \sqrt{( {x _{2} - x _{1}) }^{2} + {( {y _{2} - y _{1}) }^{2} } } \\ \\ = > \sf d = \sqrt{ ({ 4 + 1)}^{2} + { ( - 3 - 9)}^{2} } \\ \\ = > \sf d = \sqrt{ {5}^{2} + {( - 12)}^{2} } \\ \\ = > \sf d = \sqrt{25 + 144} \\ \\ = > \sf d = \sqrt{169} \\ \\ = > \boxed{ \sf{ d = 13\:units }}\\$

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Natali [406]

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3 years ago

If EF=2x-12, FG= 3x-15, and EG=23, find values of x, EF, and FG

velikii [3]

we have that

*-------------------------*--------------------------------*

E F G

EF=2x-12

FG= 3x-15

EG=23

we know that

EF + FG = EG

[2x - 12] + [3x - 15] = 23 simplify

5x - 27 = 23 add 27 to both sides

5x = 50 divide both sides by 5

x = 10

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FG= 3x-15------> FG=3*10-15------> FG=15

therefore

the answer part a) is

the value of x is 10

the answer part b) is

the value of EF is 8

the answer part c) is

the value of FG is 15

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